An open-ended lesson on number pyramids, with the potential for pupils to practice addition and subtraction with integers, decimals, negatives and fractions, form and solve linear equations in two unknowns and create conjectures and proofs. I used this lesson for an interview and got the job, so it must be a good one! The entire lesson is built around the prompt I’ve uploaded as the cover slide. I have provided detailed answers for some of the responses that pupils could give, so you can get a clear idea of how the investigation might progress. I would spend the lesson responding to pupils’ work and questions, and probably get pupils to make posters of their findings or discuss their work with other pupils. Suitable for a range of abilities. Please review if you buy as any feedback is appreciated!

A complete lesson on solving two step equations of the form ax+b=c, ax-b=c, a(x+b)=c and a(x-b)=c using the balancing method. Designed to come after pupils have solved using a flowchart/inverse operations. Activities included: Starter: A few substitution questions to check pupils can correctly evaluate two-step expressions, followed by a prompt to consider some related equations. Main: A slide to remind pupils of the order of operations for the four variations listed above. Four example-problem pairs of solving equations, to model the methods and allow pupils to try. A set of questions for pupils to consolidate, and a suggestion for an extension task. The questions repeatedly use the same numbers and operations, to reinforce the fact that order matters and that pupils must pay close attention. A more interesting, challenging extension task in the style of the Open Middle website. Plenary: A set of four ‘spot the misconception’ questions, to prompt a final discussion/check for understanding. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A challenging activity on the theme of triangle area, suitable for year 11 revision. The initial questions require a knowledge of basic triangle area, Pythagoras’ theorem, SOHCAHTOA, the sine rule and 1/2absinC so a good, challenging revision task. The questions have been designed with a ‘minimally diferent’ element, to draw pupils attention to how subtle changes can have significant implications for selecting methods. There are some follow-up questions, that could be used to shift the focus of the activity. I’d love to hear anyone’s suggestions of further questions.

Pupils solve straight forward quadratic equations to reveal a pathetic joke.

Pupils work out answers to questions on a mixture of SOHCAHTOA, sine rule, consine rule and Pythagoras’s theorem to reveal a fairly rubbish joke (although I quite like it).

A challenging set of puzzles, that mainly require pupils to use their knowledge of the properties and area rule of a parallelogram, but also involve finding areas of triangles. Includes a few ideas adapted from other sources, one of which is Don Steward’s superb Median blog, the other I’m afraid I can’t remember. Please review if you like it, or even if you don’t!

A complete lesson on solving equations of the form sinx = a, asinx = b and asinx + b = 0 (or using cos or tan) for any range. Designed to come after pupils have spent time solving equations in the range 0 to 360 degrees, and are also familiar with the cyclic nature of the trigonometric functions. See my other resources for lessons on these topics. I made this to use with my further maths gcse group, but could also be used with an A-level class. Activities included: Stater: A set of 4 questions to test if pupils can solve trigonometric equations in the range 0 to 360 degrees. Main: A visual prompt to consider solutions beyond 360 degrees. followed by a second example (see cover image) that will lead to a “dead-end” for pupils. Slides to define principal values for sine, cosine and tangent, followed by a summary of how to solve equations for any range. Three example problem pairs to model methods and then get pupils trying. Includes graphical representations to help pupils understand. A worksheet with a progression in difficulty and a challenging extension to create equations with a required number of solutions. Plenary: A prompt to discuss solutions to the extension task.

A complete lesson on the graphs of sine and cosine from 0 to 360 degrees. I’ve also made complete lessons on tangent from 0 to 360 degrees and all three functions outside the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry. Activities included: Starter: Examples to remind pupils how to find unknown angles in a right-angled triangle (see cover slide), followed by two sets of questions; the first using sine the second using cosine. The intention is that pupils estimate using the graphs of sine and cosine rather than with calculators, to refamiliarise them with the graphs from 0 to 90 degrees. Although I’ve called this a starter, this part is key and would take a decent amount of time. I would print off the question sets and accompanying graphs as a 2-on-1 double sided worksheet. Main: Slide to define sine and cosine using the unit circle, with a hyperlink to a nice geogebra to show the graphs dynamically. Or you could get pupils to try to construct the graphs themselves by visualising. A set of related questions that I would do using mini-whiteboards, where pupils consider symmetry properties of the graphs. A mini-investigation where pupils look at angles with the same sine or cosine and look for a pattern. Plenary: An image to prompt discussion about the “usual” definition of sine and cosine (using the terminology opposite, adjacent and hypotenuse) and the fuller definition (using the unit circle) Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the graphs of sine, cosine and tangent outside the range 0 to 360 degrees. I’ve also made complete lessons on these functions in the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry, and looked at the graphs of sine cosine and tangent in the range 0 to 360 degrees. This could also be used as a precursor to solving trigonometric equations in the further maths gcse or A-level. Activities included: Starter: A worksheet where pupils identify key coordinates on the graphs of sine and cosine from 0 to 360 degrees. Main: A reminder of the definitions of sine, cosine and tangent using the unit circle, with a prompt for pupils to discuss what happens outside the range 0 to 360 and a slide to make this clear. Three examples of using knowledge of the graphs to effectively solve a trigonometric equation. This isn’t formalised, but done more as a visual puzzle that pupils can answer using symmetry and the fact that the functions are periodic (see cover image). A worksheet with a set of similar questions, followed by a related extension task. Plenary: A brief summary about sound waves and how pitch and volume is determined. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the theorem that the angle at the centre is twice the angle at the circumference. For me, this is definitely the first theorem to teach as it can be derived using ideas pupils have already covered. and then used to derive some of the other theorems. Please see my other resources for lessons on the other theorems. Activities included: Starter: A few basic questions to check pupils can find missing angles in triangles. Main: A short discovery activity where pupils split the classic diagram for this theorem into isosceles triangles (see cover image). If you think this could overload pupils, it could be skipped, although I think if they can’t cope with this activity, they’re not ready for circle theorems! A link to the mathspad free tool for this topic. I hope mathspad don’t mind me putting this link - I will remove it if they do. A large set of mini-whiteboard questions for pupils to try. These have been designed with a variation element as well as non-examples, to really make sure pupils think about the features of the diagrams. A worksheet for pupils to consolidate independently, with two possible extension tasks: (1) pupils creating their own examples and non-examples, (2) pupils attempting a proof of the theorem. Plenary: A final set of six diagrams, where pupils have to decide if the theorem applies. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on the graph of tangent from 0 to 360 degrees. I’ve also made complete lessons on sine and cosine from 0 to 360 degrees and all three functions outside the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry, and have met the unit circle definitions of sine and cosine. Activities included: Starter: A quick set of questions on finding the gradient of a line. This is a prerequisite to understanding how tan varies for different angles. Main: An example to remind pupils how to find an unknown angle in a right-angled triangle using the tangent ratio, followed by a set of similar questions. The intention is that pupils estimate using the graph of tangent rather than using the inverse tan key on a calculator, to refamiliarise them with the graph from 0 to 90 degrees. Slides to define tan as sin/cos and hence as gradient when using the unit circle definition. A worksheet where pupils construct the graph of tan from 0 to 360 degrees (see cover image). A set of related questions, where pupils use graph and unit circle representations to explain why pairs of angles have the same tan. Pupils can be extended further by making and proving conjectures about pairs of angles whose tans are equal. Plenary: An image to prompt discussion about the “usual” definition of tangent (using the terminology opposite, adjacent and hypotenuse) and the fuller definition (using the unit circle) Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

Pupils are given two fractions as the start of a sequence, and try to extend it. Could be made easier or introduced using integers rather than fractions, maybe with some decimals and negatives in between. Works as either a ‘low floor high ceiling’ task, or as a way of revising different sequence types and also decimals, negatives and fractions. Particularly for the quadratic sequence, there’s scope to spend time looking at the algebra needed to find solutions. Please let me know if you can think of any other ways to extend the task!

A complete lesson on the theme of the formula for 1+2+3+…+n, looking at how the rule emerges in different scenarios. Activities included: Starter: A classic related puzzle - counting how many lines in a complete graph. After the initial prompt showing a decagon, two differing approaches to a solution are shown. These will help pupils make connections later in the lesson. This is followed by a prompt relating to the handshaking lemma, which is the same thing in a different guise. Pupils could investigate this in small groups. Main: A prompt for pupils to consider the question supposedly put to Gauss as a child - to work out 1+2+3+…+100. Gauss’s method is then shown, at which point pupils could try the same method to sum to a different total. The method is then generalised to obtain Gauss’s rule of n(n+1)/2, followed by a worksheet of related questions. These include some challenging questions requiring pupils to adapt Gauss’s method (eg to work out 2+4+6+…+100). Plenary: A final look at the sequence Gauss’s rule generates (the triangle numbers). Please review if you buy as any feedback is appreciated!

A complete lesson on the interior angle sum of a quadrilateral. Requires pupils to know the interior angle sum of a triangle, and also know the angle properties of different quadrilaterals. Activities included: Starter: A few simple questions checking pupils can find missing angles in triangles. Main: A nice animation showing a smiley moving around the perimeter of a quadrilateral, turning through the interior angles until it gets back to where it started. It completes a full turn and so demonstrates the rule. This is followed up by instructions for pupils to try the same on a quadrilateral that they draw. Instructions for pupils to use their quadrilateral to do the more common method of marking the corners, cutting them out and arranging them to form a full turn. This is also animated nicely. Three example-problem pairs where pupils find missing angles. Three worksheets, with a progression in difficulty, for pupils to work through. The first has standard ‘find the missing angle’ questions. The second asks pupils to find missing angles, but then identify the quadrilateral according to its angle properties. The third is on a similar theme, but slightly harder (eg having been told a shape is a kite, work out the remaining angles given two of the angles). A nice extension task, where pupils are given two angles each in three quadrilateral and work out what shapes they could possibly be. Plenary: A look at a proof of the rule, by splitting quadrilaterals into two triangles. A prompt to consider what the sum of interior angles of a pentagon might be. Printable worksheets and answers included throughout. Please review if you buy as any feedback is appreciated!

A brief insight into how fractals are created as well as examples in Maths, art and nature. Includes a spreadsheet to investigate. Requires a basic understanding of complex numbers to fully appreciate.

Are you bored of telling students what calculator to get for secondary school maths? Then use this poster!

Looks at switching between different bases and the effect of base on arithmetic and divisibility tests.Plus an excel 'base switch&' calculator. A good enrichment task with a historical/real-life aspect, though probably best for more able pupils.

A lesson or two of functional maths activities exploring a visual breakdown of the Budget that I found on the Guardian website recently. Requires knowledge of percentage change and reverse percentage problems. Starts with relatively straight forward calculations but gets a bit more political towards the end!

A complete lesson on vertically opposite angles. Does incorporate problems involving the interior angle sum of triangles and quadrilaterals too, to make it more challenging and varied (see cover image for an idea of some of the easier problems) Activities included: Starter: A set of basic questions to check if pupils know the rules for angles at a point, on a line, in a triangle and in a quadrilateral. Main: A prompt for pupils to reflect on known facts about angles at the intersection of two lines, naturally leading to a quick proof that vertically opposite angles are equal. Some subtle non-examples/discussion points to ensure pupils can correctly identify vertically opposite angles. Examples and a set of questions for pupils to consolidate. These start with questions like the cover image, then some slightly tougher problems involving isosceles triangles, and finally some tricky and surprising puzzles. A more investigatory task, a sort-of angle chase where pupils need to work out when the starting angle leads to an integer final angle. Plenary: An animation that shows a dynamic proof that the interior angle sum of a triangle is 180 degrees, using the property of vertically opposite angles being equal. Printable worksheets and answers included. Please do review if you buy, as any feedback is helpful!

A hyperlinked list of geogebra interactives I’ve found on a range of maths topics. Not made by me, I’m just sharing in case people find them useful.